In a large mixing bowl, whisk together 2 cups all-purpose flour, 1 tbsp baking powder, 1/2 tsp baking soda, and 1 tsp salt.

Add the 1/2 cup very cold, cubed unsalted butter to the dry ingredients. Using a pastry blender, two knives, or your fingertips, cut in the butter until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining.

Pour in the 3/4 cup cold buttermilk and mix with a fork until just combined and a shaggy dough forms. Be careful not to overmix, as this can make the biscuits tough.

Turn the dough out onto a lightly floured surface. Gently knead the dough 3-4 times, just enough to bring it together. Pat or roll the dough to about 3/4-inch thickness. Using a 2.5-inch biscuit cutter, cut out biscuits. Gently gather any dough scraps, re-pat, and cut out additional biscuits until all dough is used. You should yield 8-10 biscuits. Place the cut biscuits on a plate and refrigerate until ready to use.

In a large Dutch oven or a deep oven-safe skillet, heat 2 tbsp unsalted butter and 1 tbsp olive oil over medium-high heat.

Add the 1.5 lbs chicken pieces to the pot and cook until lightly browned on all sides, about 5-7 minutes. Remove the cooked chicken from the pot and set aside.

Reduce the heat to medium. Add the chopped yellow onion, diced carrots, and diced celery to the pot. Cook, stirring occasionally, until the vegetables soften, which takes about 8-10 minutes.

Stir in the 2 cloves minced garlic and cook for another minute until fragrant.

Sprinkle 1/2 cup all-purpose flour over the vegetables and stir well to coat, cooking for 1-2 minutes to create a roux, lightly toasting the flour.

Gradually whisk in 4 cups chicken broth, followed by 1 cup whole milk, ensuring there are no lumps. Bring the mixture to a simmer, stirring constantly, until it thickens to a gravy-like consistency.

Return the browned chicken pieces to the pot. Stir in 1 tsp dried thyme, 1/2 tsp crushed dried rosemary, and 1 bay leaf. Season generously with salt and freshly ground black pepper to taste.

Reduce the heat to low, cover the pot, and simmer for 10-15 minutes, stirring occasionally, until the chicken is cooked through and the flavors have melded. Remove the bay leaf before proceeding.

Stir in 1 cup frozen peas and cook for 2-3 minutes until they are heated through. Taste the filling and adjust seasonings as needed.

Preheat your oven to 400°F (200°C).

Arrange the chilled, prepared biscuits directly on top of the hot chicken filling in the Dutch oven or oven-safe skillet. If desired, brush the tops of the biscuits with 2 tbsp melted butter for extra golden browning.

Transfer the Dutch oven or skillet to the preheated oven and bake for 15-20 minutes, or until the biscuits are golden brown, puffed, and cooked through. Keep an eye on them to prevent over-browning.

Carefully remove the dish from the oven. Let it rest for a few minutes before serving. Garnish with fresh chopped parsley, if desired.